This example shows how to use the Least Mean Square (LMS) algorithm to subtract noise from an input signal. The LMS adaptive filter uses the reference signal on the Input port and the desired signal on the Desired port to automatically match the filter response. As it converges to the correct filter model, the filtered noise is subtracted and the error signal should contain only the original signal.
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In the model, the signal output at the upper port of the Acoustic Environment subsystem is white noise. The signal output at the lower port is composed of colored noise and a signal from a .wav file. This example model uses an adaptive filter to remove the noise from the signal output at the lower port. When you run the simulation, you hear both noise and a person playing the drums. Over time, the adaptive filter in the model filters out the noise so you only hear the drums.
The all-platform floating-point version of the model is shown below.
By running this model, we can listen to the audio signal in real time (while running the simulation). The stop time is set to infinity. This allows us to interact with the model while it is running. For example, we can change the filter or alternate from slow adaptation to fast adaptation (and vice versa), and get a sense of the real-time audio processing behavior under these conditions.
Notice the colors of the blocks in the model. These are sample time colors that indicate how fast a block executes. Here, the fastest discrete sample time (e.g., the 8 kHz audio signal processing portion) is red, and the second fastest discrete sample time is green. You can see that the color changes from red to green after down-sampling by 32 (in the Downsample block before the Waterfall Scope block). Further information on displaying sample time colors can be found in the Simulink® documentation.
The Waterfall window displays the behavior of the adaptive filter's filter coefficients. It displays multiple vectors of data at one time. These vectors represent the values of the filter's coefficients of a normalized LMS adaptive filter, and are the input data at consecutive sample times. The data is displayed in a three-dimensional axis in the Waterfall window. By default, the x-axis represents amplitude, the y-axis represents samples, and the z-axis represents time. The Waterfall window has toolbar buttons that enable you to zoom in on displayed data, suspend data capture, freeze the scope's display, save the scope position, and export data to the workspace.
You can see the details of the Acoustic Environment subsystem by double clicking on that block. Gaussian noise is used to create the signal sent to the Exterior Mic output port. If the input to the Filter port changes from 0 to 1, the Digital Filter block changes from a lowpass filter to a bandpass filter. The filtered noise output from the Digital Filter block is added to the signal coming from a .wav-file to produce the signal sent to the Pilot's Mic output port.
Haykin, S., Adaptive Filter Theory, 3rd Ed., Prentice-Hall, 1996.